I don't know about that. We live in a city where people are complaining about housing costs and availability, but the city has absolutely vast amounts of housing. We've lost close to 40% of our population since 1970.
It's just that a lot of that housing is in awful shape, and the places where it exist aren't desirable neighborhoods (although let's be clear, many of them are right next to expensive and desirable neighborhoods, it's really bad.) This should be a situation that rights itself automatically, but it's not.